At the top of the league, there is a seven-point lead over second-place Manchester City.
The visitors scored three times before Kaoru Mitoma got one back.
After Gabriel Martinelli settled any nerves, Evan Ferguson scored his first goal.
The home fans had a chance to win the game, but the second goal was ruled out to deny them a victory.
After Martinelli had restored the three-goal advantage they showed great spirit to reduce the arrears again through Ferguson.
They thought they'd made it 4-3 with two minutes left when they thought they'd scored again, but they were wrong.
With both teams having played 16 games, it's no wonder that the lead over City is growing.
This win could be a turning point in the race for a first title in a decade, as the season is not at the halfway point.
It looked like the chance of a repeat of the Carabao Cup win over Arsenal would be out of the question as soon as Saka pounced on a rebound from Martinelli's shot.
The absence of Gabriel Jesus through a knee injury he picked up while on World Cup duty may have worried fans of the club, but they are compensated by the two players.
The Norwegian's seventh goal of the season came when he capitalised on a poorhead out by Billy Gilmour to put his side 2-0 ahead before half-time.
Nketiah poked the ball in from close range after Sanchez mishandled Martinelli's shot.
The full-backs were taken out after an hour. After a good spell from the hosts, Martinelli finished off a long run with a shot that went in off the legs of the Seagulls' goalkeeper.
When Ferguson was able to pull another goal back, Mikel Arteta's side looked worried until the decision by the VAR.
Before reaching the league campaign's halfway point,Arsenal face a tough January, followed by Spurs and United.
Arteta will want to address the defensive frailties that emerged on the south coast when they meet Manchester City.
After returning from the World Cup break, the Seagulls won their first game of the season, but will regret it later.
Roberto de Zerbi's side finished strongly after capitalising on a dip in the team's performance following the substitution of White and Zinchenko.
Ferguson was a handful on his third appearance, all as a substitute, and he was smart enough to pounce on Saliba's mistake to give his side a chance of a comeback.
The Seagulls finish the year in eighth place, their highest ever finish at the end of a year.
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